The existence of that zero \(h_1^*\equiv F^{-1}(0)\)  of \(F\)  –and thus of its square \(\mathcal {F}\) –, and the analyticity required for a power series expansion (both of \(\mathcal {F}\)  and the Higgs potential \(V\) ), broadly constitute the necessary and sufficient requirements for a given HEFT Lagrangian density characterized by \(\mathcal {F}\)  to be expressible as a SMEFT.
Let us summarize and make these findings, that agree with the ones presented in [1]}, somewhat more precise:
